More than 20,000 Israeli troops entered Gaza late Thursday, hoping to clear out Hamas tunnels that can be used by terrorists to infiltrate Israel, or which warehouse rockets for Hamas and other terrorists groups.

According to Israeli military sources, the IDF hopes to secure three key areas of Gaza and deliver a crippling blow to Hamas' offensive capabilities within two weeks. They acknowledge, however, that it could take longer.

Military officials may have been caught off guard by a tunnel used by 13 heavily-armed Hamas terrorists to sneak into Israel early Thursday morning. Officials believe the 13 hoped to attack a nearby kibbutz, killing as many people as they could. Israeli military quickly discovered the infiltration and killed the terrorists as they tried to scramble back to their tunnel.

Part of the ground invasion will involve a house-to-house search in northern Gaza to find any similar tunnels. A similar search will occur in Gaza's south, near the border with Egypt, in an attempt to cut off future smuggling of weapons to Hamas and other terrorists, sources say.

The IDF made it clear that the tunnels are a priority in a Twitter post just after the invasion was announced.

The IDF also will hunt for bunkers and storage centers housing remaining rocket arsenals.

Hamas, meanwhile, issued a statement with threats and bluster. "We warn [Prime Minister Benjamin] Netanyahu of the dreadful consequences of such a foolish act," spokesman Sami Abu Zuhri said. Hamas also pledged to continue rejecting ceasefire proposals that did not yield to its demands.

Egypt, which offered a ceasefire accepted by Israel but rejected by Hamas, reportedly is still engaged in efforts to bring about a cessation of the violence. But in a remarkable statement, Egypt's foreign minister openly blamed Hamas for the ongoing violence.

"Had Hamas accepted the Egyptian proposal, it could have saved the lives of at least 40 Palestinians," Sameh Shoukri said before Israeli troops entered Gaza.

Gulf state Qatar, a Hamas ally and financial patron, is trying to join the diplomatic effort. Sources told the IPT that Qatar's efforts were endorsed by Secretary of State John Kerry, but in a British news report, an unnamed American official acknowledged that it was "unlikely that Israel would agree to Qatar as a peace broker" given its support for Hamas.

Similarly, Turkey's Prime Minister Recep Tayyip Erdogan may want to be a player in any ceasefire negotiations, but he has called Israel's retaliation against Hamas rocket fire from Gaza a "systematic genocide."

The Israeli sources told the IPT that the plan is to avoid Gaza's dense population centers and that there is no desire to occupy the entire territory.